On a sumset problem for integers

Abstract

Let $A$ be a finite set of integers. We show that if $k$ is a prime power or a product of two distinct primes then $$|A+k\cdot A|\ge (k+1)|A|-\lceil k(k+2)/4\rceil$$ provided $|A|\ge (k-1{)}^{2}k!$, where $A+k\cdot A=\{a+kb:a,b\in A\}$. We also establish the inequality $|A+4\cdot A|\ge 5|A|-6$ for $|A|\ge 5$.

arXiv commentFinal published version

References in corpus (2)

• Sums of dilates in groups of prime order
• A Lower Bound for the Size of a Sum of Dilates

Cited by in corpus (3)

• Sums of dilates in groups of prime order
• A Lower Bound for the Size of a Sum of Dilates
• Inverse problems in Additive Number Theory and in Non-Abelian Group Theory